Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class C587C {

    public static void main(String[] args) throws Exception {
        new C587C().run();
        out.close();
    }

    int[] getIntArrayFromArrayList(ArrayList<Integer> list) {
        int[] res = new int[list.size()];
        for (int i = 0; i < list.size(); ++i) {
            res[i] = list.get(i);
        }
        return res;
    }

    int[] merge(int[] l1, int[] l2) {
        int[] res = new int[Math.min(10, l1.length + l2.length)];
        int i1 = 0;
        int i2 = 0;
        int iRes = 0;
        while (iRes < res.length) {
            if (i1 < l1.length) {
                int l1V = l1[i1];
                int l2V;
                if (i2 < l2.length && (l2V = l2[i2]) < l1V) {
                    res[iRes++] = l2V;
                    ++i2;
                } else {
                    res[iRes++] = l1V;
                    ++i1;
                }
            } else {
                res[iRes++] = l2[i2++];
            }
        }
        return res;
    }

    void dfs(int v, int p, int[] h, int[][] par, int[][][] save, ArrayList<Integer>[] vList, ArrayList<Integer>[] citizens) {
        par[v][0] = p;
        save[v][0] = getIntArrayFromArrayList(citizens[v]);
        if (p != -1) {
            h[v] = h[p] + 1;
        }
        for (int i = 1; i < par[v].length; ++i) {
            if (par[v][i - 1] != -1) {
                par[v][i] = par[par[v][i - 1]][i - 1];
                save[v][i] = merge(save[v][i - 1], save[par[v][i - 1]][i - 1]);
            }
        }
        for (int u : vList[v]) {
            if (u != p) {
                dfs(u, v, h, par, save, vList, citizens);
            }
        }
    }

    int[] query(int v, int u, int[] h, int[][] par, int[][][] save) {
        if (h[v] < h[u]) {
            return query(u, v, h, par, save);
        }
        int[] res = new int[0];
        for (int i = par[v].length - 1; i >= 0; --i) {
            if (par[v][i] != -1 && h[par[v][i]] >= h[u]) {
                res = merge(res, save[v][i]);
                v = par[v][i];
            }
        }
        if (v == u) {
            return merge(res, save[u][0]);
        }
        for (int i = par[v].length - 1; i >= 0; --i) {
            if (par[v][i] != par[u][i]) {
                res = merge(res, save[v][i]);
                v = par[v][i];
                res = merge(res, save[u][i]);
                u = par[u][i];
            }
        }
        res = merge(res, save[v][1]);
        return merge(res, save[u][0]);
    }

    void run() throws Exception {
        int n = nextInt();
        int m = nextInt();
        int q = nextInt();
        ArrayList<Integer>[] vList = new ArrayList[n];
        ArrayList<Integer>[] citizens = new ArrayList[n];
        for (int i = 0; i < vList.length; ++i) {
            vList[i] = new ArrayList<>();
            citizens[i] = new ArrayList<>();
        }
        for (int i = 0; i < n - 1; ++i) {
            int a = nextInt() - 1;
            int b = nextInt() - 1;
            vList[a].add(b);
            vList[b].add(a);
        }
        for (int i = 0; i < m; ++i) {
            citizens[nextInt() - 1].add(i + 1);
        }
        int logN = 0;
        while (1 << logN < 2 * n) {
            ++logN;
        }
        int[] h = new int[n];
        int[][] par = newIntArray(n, logN, -1);
        int[][][] save = new int[n][logN][0];
        dfs(0, -1, h, par, save, vList, citizens);
        for (int i = 0; i < q; ++i) {
            int v = nextInt() - 1;
            int u = nextInt() - 1;
            int a = nextInt();
            int[] res = query(v, u, h, par, save);
            int k = Math.min(a, res.length);
            out.print(k + " ");
            for (int j = 0; j < k; ++j) {
                out.print(res[j] + " ");
            }
            out.println();
        }
    }

//~~~~~~~~~~~~~~~~~~~~~~~~~~~ template ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    int[] nextIntArray(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; ++i) {
            res[i] = nextInt();
        }
        return res;
    }

    int[][] nextIntArray(int nx, int ny) throws IOException {
        int[][] res = new int[nx][ny];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                res[i][j] = nextInt();
            }
        }
        return res;
    }

    long[] nextLongArray(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; ++i) {
            res[i] = nextLong();
        }
        return res;
    }

    long[][] nextLongArray(int nx, int ny) throws IOException {
        long[][] res = new long[nx][ny];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                res[i][j] = nextLong();
            }
        }
        return res;
    }

    int[][] newIntArray(int nx, int ny, int val) {
        int[][] res = new int[nx][ny];
        for (int i = 0; i < nx; ++i) {
            Arrays.fill(res[i], val);
        }
        return res;
    }

    int[][][] newIntArray(int nx, int ny, int nz, int val) {
        int[][][] res = new int[nx][ny][nz];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                Arrays.fill(res[i][j], val);
            }
        }
        return res;
    }

    long[][] newLongArray(int nx, int ny, long val) {
        long[][] res = new long[nx][ny];
        for (int i = 0; i < nx; ++i) {
            Arrays.fill(res[i], val);
        }
        return res;
    }

    long[][][] newLongArray(int nx, int ny, int nz, long val) {
        long[][][] res = new long[nx][ny][nz];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                Arrays.fill(res[i][j], val);
            }
        }
        return res;
    }

    String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            strTok = new StringTokenizer(in.readLine());
        }
        return strTok.nextToken();
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    static StringTokenizer strTok;
    final static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    final static PrintWriter out = new PrintWriter(System.out);
}